Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm

Osuji; George A.; Okoli Cecilia N.; Opara; Jude

doi:doi:10.11648/j.sjams.20140204.11

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Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm

Osuji, George A., Okoli Cecilia N., Opara, Jude

Published in Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 4)

Received: 9 July 2014 Accepted: 15 July 2014 Published: 30 July 2014

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Abstract

This paper is on the solution of multi-objective transportation problem via fuzzy programming algorithm. The data for this paper was collected by an egg dealer in whose main office is located at Orji Owerri Imo State Nigeria, who supplies the product to different wholesalers (destinations) after taking it from different poultry farm (sources), and the time and cost of transportation from source i to destination j were recorded. TORA statistical software was employed in the data analysis, and the results of the analysis revealed that if we use the hyperbolic membership function, then the crisp model becomes linear. The result also revealed that the optimal compromise solution does not alter if we compare it with the solution obtained by the linear membership function. Thus, if we compare it with the solution obtained by the linear membership function, it is shown that the fuzzy optimal values do not depend on the chosen membership function be it linear or non-linear membership function.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 2, Issue 4)
DOI	10.11648/j.sjams.20140204.11
Page(s)	71-77
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

MOTP, Transportation Problem, Fuzzy Programming Algorithm, Hyperbolic Membership Function, Linear Membership Function, Optimization Problem

References

[1]	Lau, H. C.W., Chan, T.M., Tsui, W. T., Chan, F. T. S., Ho, G. T. S. and Choy, K. L., A (2009): fuzzy guided multi-objective evolutionary algorithm model for solving transportation problem, Expert System with Application: An International Journal, Vol. 36,2009, pp.8255-8268.
[2]	Osuji G. A. Opara J., Nwobi A. C., Onyeze V., Iheagwara A. I.(2013): Paradox Algorithm in Application of a Linear Transportation Problem. American Journal of Applied Mathematics and Statistics, 2014, Vol. 2, No. 1,10-15. DOI:10.12691/ajams-2-1-3
[3]	Surapati, P. and Roy, T. K. (2008). Multi-objective transportation model with fuzzy parameters: Priority based fuzzy goal programming approach, Journal of Transportation System Engineering and Informational Technology, Vol. 8, 2008, pp 40-48
[4]	Wahed, W. F. and Lee, S. M. (2006). Interactive fuzzy goal programming for multi-objective transportation problems, Omega, Vol. 34, 2006, pp. 158-166.
[5]	Zangiabadi, M. and Maleki, H. R. (2007). Fuzzy goal programming for multi-objective transportation problems, Applied Mathematics Computation, Vol. 24-2007, pp. 449-460.

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APA Style

Osuji, George A., Okoli Cecilia N., Opara, Jude. (2014). Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm. Science Journal of Applied Mathematics and Statistics, 2(4), 71-77. https://doi.org/10.11648/j.sjams.20140204.11

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ACS Style

Osuji; George A.; Okoli Cecilia N.; Opara; Jude. Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm. Sci. J. Appl. Math. Stat. 2014, 2(4), 71-77. doi: 10.11648/j.sjams.20140204.11

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AMA Style

Osuji, George A., Okoli Cecilia N., Opara, Jude. Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm. Sci J Appl Math Stat. 2014;2(4):71-77. doi: 10.11648/j.sjams.20140204.11

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@article{10.11648/j.sjams.20140204.11,
  author = {Osuji and George A. and Okoli Cecilia N. and Opara and Jude},
  title = {Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {2},
  number = {4},
  pages = {71-77},
  doi = {10.11648/j.sjams.20140204.11},
  url = {https://doi.org/10.11648/j.sjams.20140204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140204.11},
  abstract = {This paper is on the solution of multi-objective transportation problem via fuzzy programming algorithm. The data for this paper was collected by an egg dealer in whose main office is located at Orji Owerri Imo State Nigeria, who supplies the product to different wholesalers (destinations) after taking it from different poultry farm (sources), and the time and cost of transportation from source i to destination j were recorded. TORA statistical software was employed in the data analysis, and the results of the analysis revealed that if we use the hyperbolic membership function, then the crisp model becomes linear. The result also revealed that the optimal compromise solution does not alter if we compare it with the solution obtained by the linear membership function. Thus, if we compare it with the solution obtained by the linear membership function, it is shown that the fuzzy optimal values do not depend on the chosen membership function be it linear or non-linear membership function.},
 year = {2014}
}

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TY  - JOUR
T1  - Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm
AU  - Osuji
AU  - George A.
AU  - Okoli Cecilia N.
AU  - Opara
AU  - Jude
Y1  - 2014/07/30
PY  - 2014
N1  - https://doi.org/10.11648/j.sjams.20140204.11
DO  - 10.11648/j.sjams.20140204.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 71
EP  - 77
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20140204.11
AB  - This paper is on the solution of multi-objective transportation problem via fuzzy programming algorithm. The data for this paper was collected by an egg dealer in whose main office is located at Orji Owerri Imo State Nigeria, who supplies the product to different wholesalers (destinations) after taking it from different poultry farm (sources), and the time and cost of transportation from source i to destination j were recorded. TORA statistical software was employed in the data analysis, and the results of the analysis revealed that if we use the hyperbolic membership function, then the crisp model becomes linear. The result also revealed that the optimal compromise solution does not alter if we compare it with the solution obtained by the linear membership function. Thus, if we compare it with the solution obtained by the linear membership function, it is shown that the fuzzy optimal values do not depend on the chosen membership function be it linear or non-linear membership function.
VL  - 2
IS  - 4
ER  -

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Author Information

Osuji
George A.
Okoli Cecilia N.

Department of Statistics, Anambra State University, PMB 02, Uli Anambra State
Opara
Jude

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Plain Text BibTeX RIS

APA Style

Osuji, George A., Okoli Cecilia N., Opara, Jude. (2014). Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm. Science Journal of Applied Mathematics and Statistics, 2(4), 71-77. https://doi.org/10.11648/j.sjams.20140204.11

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ACS Style

Osuji; George A.; Okoli Cecilia N.; Opara; Jude. Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm. Sci. J. Appl. Math. Stat. 2014, 2(4), 71-77. doi: 10.11648/j.sjams.20140204.11

Copy | Download

AMA Style

Osuji, George A., Okoli Cecilia N., Opara, Jude. Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm. Sci J Appl Math Stat. 2014;2(4):71-77. doi: 10.11648/j.sjams.20140204.11

Copy | Download

@article{10.11648/j.sjams.20140204.11,
  author = {Osuji and George A. and Okoli Cecilia N. and Opara and Jude},
  title = {Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {2},
  number = {4},
  pages = {71-77},
  doi = {10.11648/j.sjams.20140204.11},
  url = {https://doi.org/10.11648/j.sjams.20140204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20140204.11},
  abstract = {This paper is on the solution of multi-objective transportation problem via fuzzy programming algorithm. The data for this paper was collected by an egg dealer in whose main office is located at Orji Owerri Imo State Nigeria, who supplies the product to different wholesalers (destinations) after taking it from different poultry farm (sources), and the time and cost of transportation from source i to destination j were recorded. TORA statistical software was employed in the data analysis, and the results of the analysis revealed that if we use the hyperbolic membership function, then the crisp model becomes linear. The result also revealed that the optimal compromise solution does not alter if we compare it with the solution obtained by the linear membership function. Thus, if we compare it with the solution obtained by the linear membership function, it is shown that the fuzzy optimal values do not depend on the chosen membership function be it linear or non-linear membership function.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Solution of Multi-Objective Transportation Problem Via Fuzzy Programming Algorithm
AU  - Osuji
AU  - George A.
AU  - Okoli Cecilia N.
AU  - Opara
AU  - Jude
Y1  - 2014/07/30
PY  - 2014
N1  - https://doi.org/10.11648/j.sjams.20140204.11
DO  - 10.11648/j.sjams.20140204.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 71
EP  - 77
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20140204.11
AB  - This paper is on the solution of multi-objective transportation problem via fuzzy programming algorithm. The data for this paper was collected by an egg dealer in whose main office is located at Orji Owerri Imo State Nigeria, who supplies the product to different wholesalers (destinations) after taking it from different poultry farm (sources), and the time and cost of transportation from source i to destination j were recorded. TORA statistical software was employed in the data analysis, and the results of the analysis revealed that if we use the hyperbolic membership function, then the crisp model becomes linear. The result also revealed that the optimal compromise solution does not alter if we compare it with the solution obtained by the linear membership function. Thus, if we compare it with the solution obtained by the linear membership function, it is shown that the fuzzy optimal values do not depend on the chosen membership function be it linear or non-linear membership function.
VL  - 2
IS  - 4
ER  -

Copy | Download